Reconfigurable memlogic long wave infrared sensing with superconductors

Optical sensors with in-cell logic and memory capabilities offer new horizons in realizing machine vision beyond von Neumann architectures and have been attempted with two-dimensional materials, memristive oxides, phase-changing materials etc. Noting the unparalleled performance of superconductors with both quantum-limited optical sensitivities and ultra-wide spectrum coverage, here we report a superconducting memlogic long-wave infrared sensor based on the bistability in hysteretic superconductor-normal phase transition. Driven cooperatively by electrical and optical pulses, the device offers deterministic in-sensor switching between resistive and superconducting (hence dissipationless) states with persistence > 105 s. This results in a resilient reconfigurable memlogic system applicable for, e.g., encrypted communications. Besides, a high infrared sensitivity at 12.2 μm is achieved through its in-situ metamaterial perfect absorber design. Our work opens the avenue to realize all-in-one superconducting memlogic sensors, surpassing biological retina capabilities in both sensitivity and wavelength, and presents a groundbreaking opportunity to integrate visional perception capabilities into superconductor-based intelligent quantum machines.


Additional data of electrical characterizations
The critical temperature of the device is measured with a small constant bias current of 1 μA and a four-probe method, revealing that the superconducting state is completely disrupted at approximately 7.3 K, as displayed in Fig. S1a.
To assess the reliability and endurance of our memlogic devices, we conducted an endurance experiment wherein an electrical pulse (400 μA and 0.1 s duration) is applied during the program process, while a smaller electrical pulse (1 μA and 0.1 s duration) is involved for reset process, and HRS/LRS are read under a bias current of 200 μA.
The on/off ratio reached up to 10 3 over 10 6 cycles, as illustrated in Fig. S1b.At lower temperatures, theoretically, this on/off ratio can be infinite because of zero resistance in the superconducting state.The HRS/LRS remained steady as a function of the cycle number, demonstrating the robustness of our memlogic sensor's memory.
We also assessed the time response of switching the HRS and LRS.A series of 10 KΩ resistance is utilized to generate a small constant bias current within a low voltage supply.The program process and reset process, which lasted for 10 μs, operated with high voltage of 5 V and low voltage of 0.1 V respectively, as produced by arbitrary function generator.Under high electrical pulse, the device's voltage attained a plateau within 2.2 μs whereas it dropped back to zero under low electrical pulse in just 1.9 μs, as shown in Fig. S1c.

Simulation of electrical field distribution
The finite-difference time-domain (FDTD) method is implemented for the simulation in which we set the permittivity of Si ε = 11.9, and the permeability constant b The z-x plane electric field distribution.

Tunable optical properties of metamaterials
The resonant wavelength of metamaterial is easily tunable by adjusting the width of Nb wire, as demonstrated in Fig. S3a and S3b while maintaining fixed Nb and Si thickness and period.The width of Nb wire is tuned form 0.8 μm to 1.3 μm.The resulting absorption spectrum of each varied width is displayed in Fig. S3a.A trend line between the wavelength and width is plotted from extracted resonant wavelengths in Fig. S3a, as presented in Fig. S3b.As discussed in the main text, there exists a linear dependence between Nb wire width and resonant wavelength (Fig. S3b).
Metamaterial's absorption intensity can be adjusted by changing the period of the material, as depicted in Fig. S3c.The resonant absorption intensity initially increases with increased period but declines following peak absorption at a period of 2 μm.

Time response of optical switching characteristic
We measured the optical switching characteristic's time response by recording voltage time traces, as depicted in Fig. S4, using an oscilloscope at 6.5 K, constant voltage source (9 V), and a 100 kΩ resistance in series.The infrared light (12.2 μm, 0.66 mW cm −2 ) is modulated by a chopper for on-off signal processing.
Writing and erasing via light resulted in response times of 5.4 ms and 4.5 ms respectively.This time response of optical switching is slower than electrical switching.
The response time of switching main contain the thermal relaxation and electrical recovery time  =   ⁄ , where the  is kinetic inductance of Nb wire, R is the normal state resistance.The light radiation not only heats up the Nb wire but also the substrate, potentially prolonging the thermal relaxation time compared to electrical switching.
Operational speed can be further improved by reducing the device's size, thereby decreasing resistance and parasitic inductance/capacitance.Additionally, drawing from the concept of the Joule heat superconducting device 2 , a novel approach could enhance the speed to the thermal relaxation time (~ns).This involves replacing the metallic electrical heater in the htron with an optical antenna, commonly used to harvest light and generate local hotspots [3][4][5] .

Temperature and light power dependence of hysteresis and mechanism
We begin by considering a simple one-dimensional model appropriate to bridges which are much longer than the thermal healing length .The typical thermal healing length is of order 5 μm.Heat generated in localized dissipative regions in such bridges is transferred in two ways: by thermal conduction within the film and by surface heat transfer across the temperature discontinuity which develops at the boundary with the substrate (and with the helium bath, if present).Because the dimensions of the microbridges are very small compared to the dimensions of the substrate, the substrate may be assumed to be essentially at the ambient temperature   .We assume a bridge of length  , width  , and thickness  with a normal region of length 2  and resistivity  , symmetrically centered in the bridge.The temperature distribution () along the bridge must satisfy the heat-flow equations 6 : where   and   are the thermal conductivities of the wire in the normal and superconducting states, respectively.α is the total heat transfer coefficient per unit area of film, and  is the current flowing through the bridge.The temperature at ±  is assumed to be   .The temperature profile along the wire, (), is solved for assuming that the heat flow at ±  is continuous, and  ≈   as  → ±∞ .By solving for a range of   , we can trace out a current-voltage (IV) curve that contains a distinct region of near-constant current for a range of voltages.This current is the hotspot current,   .
When the hotspot is sufficiently long, in our case, the entire wire is in normal state with constant temperature   due to Joule heating, such that  2   2 ≈ 0, allowing us to drop the first term on the left-hand side of (1): Thus, we can get the retrapping current   = ( 2   /) 1/2 (1 − /  ) 1/2 without illumination of light.This is the threshold current that can keep the entire wire normal state due to Joule heating.When the bias current smaller than   , the wire will be superconducting state.
The above equation ( 3) can also be rewritten as 7 : Where the   is the sheet resistance in the normal state.
Next, when we illuminate the light on wire, another heating source caused by light power needed to be consider into the heat-flow equations.Thus, the equation ( 4) can be modified as: Where  is an adjustable parameter, P is incident light power density, S is the area of sensor.We can get the modified retrapping current   () 2 =  2 (  −   )   ⁄ − • .

The simulation of heat transfer
We use the Multiphysics software to simulated the thermal balance physics to further verify our hot spot model.In our model, the substrate is assumed to be essentially at the ambient temperature Tb, due to the dimensions of the substrate is very lager compared to the area of nanowire sensor.
The Joule heating is the only heating source.The Joule heating would be transfer into the substrate.
The interface of thermal conductivity  = 5. 6 W cm −2 K −1 .The geometry of Nb nanowire is set the same as the experiment data, width W=1.3 μm, length  = 100 μm and period  = 2.5 μm.
The resistivity of Nb wire is also the same as measurement data  = 1.56 × 10 −7 Ωm.When we set different input current   and different ambient temperature   , it would generate new thermal balance temperature T alone the nanowire sensor.When the temperature of nanowire larger than the critical temperature   ，the nanowire sensor is in normal state with normal resistance, otherwise the nanowire sensor is in superconducting state with zero resistance.When we set the temperature of nanowire equal to   , we can obtain a serials of ambient temperature   and input current .This simulation data is quite agreed with our experimental data and theory (Fig. S5).

The memlogic characteristic with three intensities of light
We measure the IV curves under light illumination with three different power densities of 0 (light off), 1(0.4 mW cm -2 ), and 2(0.65 mW cm -2 ) at 6.5 K, as shown in

Schematic diagram of parallel information transmission in memlogic arrays
We use a memlogic sensor to simulate the parallel information transmission.The schematic diagram of this parallel information transmission technology is shown in Fig. S8.Suppose an array with five sensors work at different bias current regions.We can obtain five different images under the same beam of light illumination.

Schematic diagram of ANN memlogic array
Our infrared memlogic device can be used for more complex and intelligent applications, such as Artificial Neural Networks (ANN).Figure S9a is  We provide several methods for controlling the weight resistance   : 1. Independent bias current source control: Each device has an independent current source, and when the devices operate with different bias currents, their responses to light also vary, as shown in Fig 4 .2. Devices in the same column share the same bias current, but each device has an independent gate voltage to control the adjacent superconducting nanowires, similar to MIT's Tron 8 .
3. Devices in the same column share the same bias current, but each device has independent control over temperature using metal heating wires, similar to MIT's htron 2 .
The diagram depicted in the Fig. S9b illustrates a schematic representation of an Artificial Neural Network (ANN) that relies on bias current modulation.The following readout circuitry employs CMOS-based adders and comparators, facilitating the aggregation of weighted products derived from the light responses.The output is produced when a predetermined threshold voltage is attained.
We can also use localized temperature to adjust the weight of each pixel.In this scenario, each column of unit devices is connected in series and supplied with the same current (Ibias).The output voltage is the sum of voltages across all devices.Each device has its own separate control current or voltage to generate localized hotspots, thereby individually heating each unit device.This allows for the independent control of the critical current Ic and Ir of each unit device, effectively adjusting their weights.
Furthermore, as discussed in Fig. 6, our device, when operating at a specific bias current, exhibits a threshold response to light.It produces a substantial response only when the light intensity surpasses this threshold.Consequently, our hardware design encompasses adjustable weights, threshold responses, and summation operations, which constitute the foundational components of an artificial neural network (ANN).
Moreover, an intriguing aspect is that if each unit device possesses a distinct normal-state resistance (achievable through minor adjustments in device length during fabrication), we can discern which unit device in a column responds to light using just one readout voltage, denoted as V1.Conversely, traditional array detectors would necessitate at least N readout circuits to individually assess the voltages of N devices in the same column and pinpoint the specific unit device.
Our device also boasts wavelength tunability and scalability.We manipulate light through metamaterial and metasurface technologies.Our device incorporates metamaterial technology, enabling us to finely adjust its resonance response wavelength.
As elucidated in supplementary Note 3, by manipulating the device's geometric parameters, we can customize the resonance wavelength to our desired band.
Consequently, we can set different response wavelengths for each unit device.In the scenario where a sizable light spot simultaneously illuminates all the devices, only those devices resonating with the incident light will respond and yield an output.Therefore, our device can directly extract spectral information using a single voltage readout circuit.Furthermore, by integrating metasurface technology, we can spatially segregate light of varying color wavelengths, directing them onto distinct unit devices.This enhances light utilization efficiency and diminishes crosstalk.

Potential application of memlogic arrays
The following diagram illustrates our device's capacity to emulate the focusing and memory functions of the human eye.In a scenario with a uniform light intensity field, such as the three letters "FDU" emitting light with equal intensity, we focus on distinct information, resulting in varied reading and storage outcomes.As depicted in our experiment (Fig. S10), when letters share the same light intensity, our devices initially operate at identical bias currents and generate indistinguishable signals.However, if our devices have undergone training, akin to the way our brains prioritize specific points in a scene and direct our gaze to those points (by increasing the bias current in a particular region of the array to attain a bistable state with memory, biasing the detector in the "FD" region to the "D" current region), this enhances the perception and memory of the region of interest, mimicking the human eye.
Even over time, our brains retain memory of the area of interest (the letters "FD") while selectively disregarding other details in the same scene (like the letter "U" with bias current in region C).The experiment validates that our detector possesses a focusing and memory capability akin to that of the human eye.This ability can serve as preprocessing for visual information, enabling the detector to selectively store target information, filter out superfluous data, leading to reduced energy consumption, preserved storage space, and enhanced efficiency in subsequent, more intricate computational tasks.Moreover, even at the individual device level, we can perform some simple image preprocessing functions.Simply convert a two-dimensional image into a onedimensional array input to a laser, and then transmit it to the detector (Fig. S11).The signal perceived by the detector will filter out some noise points, as shown in the diagram below.At this point, our device operates under a constant current, and its noise filtering principle is illustrated in fig.6.By filtering out noisy images, subsequent image recognition algorithms can reduce the number of training computations, decrease power consumption, and improve accuracy, as demonstrated by many researchers 9 .If the array was made, this process will be more efficiency.

Figure
Figure S1 Additional data of electrical characterizations.a The resistance-temperature curve show the critical temperature is about 7.3 K. b Endurance characteristics of memlogic sensor, showing no error during 10 6 pulse cycle.The HRS is programmed by high current pulse (400 μA, duration of 0.1 s), and the reset process is initiated by a low current pulse (1 μA, duration of 0.1 s), read by current 200 μA.c Time response of switching the HRS and LRS.The grey square wave voltage is generated by arbitrary function generator with low level 0.1 V and high level 5 V.

µ = 1 .
Figure S2 Simulation of electric field distribution.a The x-y plane electric field distribution.

Figure
Figure S3 Tunable optical properties of metamterials a The absorption spectrum of different width of metamaterial.b The resonant of wavelength dependent on width of metamaterial.c The absorption spectrum of different period of metamaterial.

Figure
Figure S4 Time response of optical switching characteristic.a It is recorded by oscilloscope at 6.5 K with constant voltage series with 100 kΩ resistance.The light on-ff is modulated by chopper.b The response time of writing and erasing by light is 5.4 ms and 4.5 ms, respectively

Figure𝐼
Figure S5 The retrapping current vs temperature.Inset: the simulation of temperature distribution of cross section of one period of Nb wire and substrate.The temperature of substrate   =6.5 K, the bias current   =0.2 mA.

Figure S6
Figure S6 The critical current suppressed by intensity of light.When the light intensity exceeds a certain value, the current decreases with the increase of the light intensity.

Fig. S7a .
Fig.S7a.Different output states are obtained when operating at various bias current zones despite receiving the same light input.In the case of three intensity of light, we can define three operating bias current zone, corresponding to A, B, C in Fig.S7a.The three different output state and logic truth table is shown in Fig.S7b.When an encrypted letter "B" image with three different intensities of light transmit to sensor by laser, we can decode to a letter "L", "E" or "B" through operating the sensor at different bias current A, B or C, respectively.(Fig.S7)

Figure
Figure S8 Schematic diagram of parallel information transmission in memlogic arrays.The information, which contained N=4 different intensity of light, is detected simultaneously by five memlogic sensor at different bias current.Then, five different images are obtained by five sensors, respectively.
a simplified diagram of a software-based ANN model, consisting of multiple neurons connected to each other through adjustable connection weights   .The output Y depends on the weighted sum of inputs from preceding neurons and needs to accumulate to a certain threshold before outputting.Our device can be used for hardware implementations of ANN, as shown in the Fig. S9b and Fig. S9c.In our system, the output of the neural network can be expressed as   = (∑     ), where the weights   are represented by the light-responsive resistance   of superconducting nanowires.Since the lightresponsive resistance   of superconducting nanowires exhibits highly nonlinear behavior, it can be controlled by adjusting bias current, light intensity, and temperature.

Figure
Figure S9 Schematic diagram of ANN arrays.a The Schematic diagram of software-based Artificial Neural Network (ANN).b The schematic diagram illustrates a superconducting nanowire ANN array with independent bias currents at each pixel, allowing for the adjustment of each pixel's weight.The output voltage is dependent on the summation of voltages from each pixel and the threshold voltage.c The Schematic diagram of superconducting nanowire ANN array with the same bias current at each pixel, but different local temperature at each pixel to adjust weight.The diagram on the left portrays each pixel designed to function at an identical operational wavelength, while the diagram on the right illustrates each pixel having a distinct detection wavelength.However, by designing the normal state resistance of each device differently, it becomes possible to infer the specific detected wavelength and spatial position information from the read voltage.

Figure
Figure S10Emulate the focusing and memory functions of the human eye by memlogic array.The "FD" and "U" pixels were operated at different bias currents, with the "FD" pixel of the sensor being operated in a bistable state, exhibiting memory functionality.

Figure
Figure S11 Preprocessing the image in-sensor.The memlogic sensor has the function of filter.